diff --git a/geopandas/geoseries.py b/geopandas/geoseries.py
index d1b1b1a..03b4f07 100644
--- a/geopandas/geoseries.py
+++ b/geopandas/geoseries.py
@@ -135,6 +135,33 @@ class GeoSeries(Series):
             return Series([s.contains(other) for s in self],
                           index=self.index)
 
+    # TODO: refactor to eliminate replications
+    def difference(self, other):
+        """
+        Return a GeoSeries of differences
+        Operates on either a GeoSeries or a Shapely geometry
+        """
+        if isinstance(other, GeoSeries):
+            # TODO: align series
+            return GeoSeries([s[0].difference(s[1]) for s in zip(self, other)],
+                          index=self.index)
+        else:
+            return GeoSeries([s.difference(other) for s in self],
+                          index=self.index)
+
+    def union(self, other):
+        """
+        Return a GeoSeries of differences
+        Operates on either a GeoSeries or a Shapely geometry
+        """
+        if isinstance(other, GeoSeries):
+            # TODO: align series
+            return GeoSeries([s[0].union(s[1]) for s in zip(self, other)],
+                          index=self.index)
+        else:
+            return GeoSeries([s.union(other) for s in self],
+                          index=self.index)
+
     def buffer(self, distance, resolution=16):
         return GeoSeries([geom.buffer(distance, resolution) for geom in self],
                          index=self.index)